Properties

Label 39.2.b
Level $39$
Weight $2$
Character orbit 39.b
Rep. character $\chi_{39}(25,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $9$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 39.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(39, [\chi])\).

Total New Old
Modular forms 6 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

Trace form

\( 2 q - 2 q^{3} - 2 q^{4} + 2 q^{9} + 2 q^{12} - 2 q^{13} + 12 q^{14} - 10 q^{16} - 12 q^{17} + 12 q^{22} + 10 q^{25} - 12 q^{26} - 2 q^{27} + 12 q^{29} - 2 q^{36} - 12 q^{38} + 2 q^{39} - 12 q^{42} - 8 q^{43}+ \cdots - 12 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(39, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
39.2.b.a 39.b 13.b $2$ $0.311$ \(\Q(\sqrt{-3}) \) None 39.2.b.a \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{2}-q^{3}-q^{4}+\beta q^{6}+2\beta q^{7}+\cdots\)